Since the release of Amores Perros in 2000, Mexican film-makers have been getting a lot of attention. According to Vanessa Bauche, who starred opposite Gael García Bernal in that film, everyone appreciates Mexican cinema – except the Mexicans. "People think the situation in Mexico is really ‘woo-woo!’" she says, in her occasionally tentative English, "but that’s not true. Alejandro González Iñárritu is very successful but Amores Perros is the only film he’s made in Mexico. Gael is coming back to Mexico now, but Alfonso Cuarón [who directed Harry Potter and the Prisoner of Azkaban] hasn’t lived in Mexico for 10, 15 years. Even though we have a lot of talented people, we don’t have an industry."

It’s a frustrating situation, and one she hopes might change with the season of Mexican cinema now on at the National Film Theatre in London. Bauche says that Mexicans pay more attention to what’s happening abroad than to their own arts scene: it’s how they decide who to pay attention to. "Unless you’re on the TV or a pop star," she says, "you have to be exported first to be imported back to your country. When someone outside says you’re good, that’s when your own people recognise you."

Although she appears in three films in the NFT festival, Bauche is in London to perform in On Insomnia and Midnight, a new play by Edgar Chías at the Royal Court, part of the theatre’s Arena Mexico season. If anything, Mexican theatre is even less valued and supported at home than its cinema: no wonder Bauche sees Arena Mexico as a bridge between Britain and her country that "has to be walked for as long as we can sustain it".

She’s still surprised that, four years since she last performed in a theatre, she was picked to play the woman in On Insomnia and Midnight – a two-hander that explores the position of men and women in society. And yet the part is typical of the roles Bauche tends to play. "I don’t know if the characters look for me or if I look for my characters," she says. "But I do like to play strong women, characters that don’t offend or degrade women."

Bauche’s pretty features and generously chatty nature could mislead you into thinking that she’s a soft touch. There’s a fierceness to this 33-year-old actor, especially when she talks about social, cultural and sexual inequality. She’s been a professional actor since the age of 13, when she began performing in musicals and soap operas while attending drama school. Then, at 14, her mother took her to a festival of work by the Mexican 1960s new wave. "These were brave films," Bauche remembers, "very important, very socially committed. That was when I realised what I wanted to do."

She got her first film role three years later, as a drug-addicted prostitute in Alex Cox’s Highway Patrolman. Fifteen years after that, she finally got to work with Felipe Cazals, one of the film-makers who had most inspired her in her youth, on Digna: Hasta el Ultimo Aliento, an investigation into the death of celebrated human rights lawyer Digna Ochoa, who was shot dead in her office on October 19 2001.

If 14 sounds like a young age at which to settle on a career in challenging cinema, Bauche thinks her "bohemian" upbringing made this maturity essential. Her mother was just 16 when she married Bauche’s father, a Gypsy almost twice her age; the couple divorced a decade later, when Bauche was seven. She and her younger brother Tito spent three years travelling with their father before settling with their mother in Mexico City. For the children, the divorce was "a release: as a kid you can feel when something is wrong, so when you feel that your parents are relaxed and happy, even if they’re not together any more, it’s OK".

Her family background also made a performing career inevitable. Her mother had children too young to be able to fulfil her own ambition to be a singer and dancer. Her father, though, was an opera student who became smitten with bossa nova after a visit to Brazil at the age of 18; now in his mid-60s, he’s been performing "African and Latin soul" ever since. Bauche’s brother is also a musician and songwriter; Vanessa, though, was more influenced by the movies her parents showed her on video. It’s partly because of these films that her English is so fluent: she would practise acting by imitating Dustin Hoffmann, Al Pacino and Meryl Streep. Perhaps the film that struck her most, though, was Karel Reisz’s Isadora, starring Vanessa Redgrave as the dancer Isadora Duncan – not least because it’s after Redgrave that Bauche is named.

Since she arrived in London, one of the things that has excited Bauche most has been the prospect of Redgrave coming to see the show. More importantly, she hopes that working here will transform her professional life in Mexico. Although she declares herself contented with her 20-year career, she admits that, financially, "it’s a miracle" she survives. She would rather struggle, though, than compromise. "Films for me are my lover and my sons and my daughters," she says. "My projects are more than just a job: they’re my creations. That’s why I’m selective with what I do. Success is important, money is important – but not enough to make you do insulting things".

· On Insomnia and Midnight opens at the Royal Court, London SW1 (020-7565 5000), on Friday. Mexican Cinema Now is at the National Film Theatre, London SE1 (020-7928 3232), until October 18.